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acot(-x) evaluation #10995

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SteliosStefanatos opened this Issue Apr 10, 2016 · 2 comments

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SteliosStefanatos commented Apr 10, 2016

In Sympy (ver. 1.0), the following input

var('x'); acot(-x)

gives

-acot(x)

which does not hold. (It actually holds acot(-x) = pi - acot(x).)

@leosartaj leosartaj added the valid label Apr 11, 2016

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leosartaj commented Apr 11, 2016

This appears valid. According to the wikipedia article it should be acot(-x) = pi - acot(x). @SteliosStefanatos, if you want you should go ahead and fix this. 😄

skirpichev added a commit to diofant/diofant that referenced this issue Apr 11, 2016

Add notes about acot definition
Wiki article must be fixed eventually.  Meanwhile, move
this reference down.  Closes sympy/sympy#10995
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postvakje commented Apr 11, 2016

I guess it depends on how the principal branch of acot is defined. In Wikipedia, the branch covering (0,pi) is used and thus acot(-x) = pi - acot(x), but Mathematica uses the branch covering (-pi/2, pi/2) with a discontinuity at x = 0, so in that case acot(-x) = -acot(x) which is also the definition used by NIST/DLMF.

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